Southern Utah with kids

Your profile says Seattle, is that the start point? Do you have a proposed route yet? I'm asking as you might want a stop or two to let them run and burn off some P&V. How much time do you have?

There is some good sounding water parks in the greater SLC area when I was researching for a similar trip with the grandkids.

I'm sending you a PM.

So much depends on the season and your intended route, but here are some ideas:
(note that my brain seems to be working from South to North today, so adjust as needed)

A few miles west of Marble Canyon off Hwy 89A then about 2 miles north up House Rock Valley Road, is a Condor Viewing site. A few more miles north on House Rock Valley Road, is a nice hike to some pictographs. If you have a 4x4 and are adventuress, check out White Pocket in the same area. Awesome place, but do use caution (if you try to go to White Pocket), as there can be deep sand in there.
Condors can also sometimes be seen under the bridge and cliffs at Marble Canyon (just park at the visitor center and walk out on the old bridge. Nice NPS CG at Lees Ferry.

A few miles north of Kanab, off the East side of hwy 89, there are Dinosaur Tracks. It's a bit weird parking at a truck stop/weigh station, and then you gotta figure out the trail to the top of the ridge (not marked, but lots of folks have walked there so there is a "route". Up on the ridge you will find the tracks. A little imagination (and some water to lightly spread over the tracks) helps.

A little further to the north and east, Escalante is the best. You could spend a lifetime exploring the region (I have been doing just that). Research Spooky and Peek-a-Boo canyons, check out hike up to Calf Creek falls (don't miss the large picto's), walk along (and in) the river to several arches, lots of petrified wood down the Burr Trail (you can drive it) past Deer Creek CG. Personally, I would stay at the large BLM dispersion camping area about a mile down (south) Hole-in-the-Rock Road when exploring the area or stay at Kodachrome Basin State Park (or one of the several RV parks in the area if that is more your style. Soooo many places to explore here. Much, much, much better than the Big Ditch (Grand Canyon).

I could go on and on, but then you would miss the fun of researching and finding special places for yourself. But these should give you some starting points.

Have fun.

Coral Pink Sand Dunes state park should be a hit with the kids. Zion and Arches can be very hot and very packed. Canyonlands is usually comparatively empty and has boondocking. Dead Horse State Park is another good spot. Lots of boondocking east of Arches.
Escalante has lots of slot canyons and Hole in the Wall. Boondocking in the NF. Kodachrome SP. Bryce not quite as crowded and lots of Boondocking in the surrounding area and two campgrounds inside the park. Much cooler too.